An accurate and efficient numerical method of solving the radial Schrödinger equation for a diatomic molecule has been employed in two tests relating to approximate potential functions. First, quantitative estimates have been made of the errors in the approximate eigenvalue equation derived by Pekeris for the rotating Morse oscillator. Secondly, as an example of testing a potential function for which no analytic solution is known, the eigenvalues of the Clinton potential have been compared with those of the Morse and with experiment.

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An empirical potential surface for the hydrogen exchange reaction is derived from the simplest form of the London approximation (neglecting overlap), by evaluating the Coulomb and exchange integrals from the potential curves for the 1Σg+ and 3Σu+ states of H2. This procedure gives an activation energy of 8.9±1.2 kcal/mole, in good agreement with the experimental value of 8.0±0.5 kcal/mole. The potential surface has a single saddle point, and the H: complex is linear and symmetrical, with a bond length of 0.96 Å. Simple, explicit formulas for the activation energy and the vibrational force constants are also obtained. The results emphasize the important contribution from the triplet repulsion between the end atoms with parallel spins in the complex.